Well, according to news and gossip site Latino Review, Disney has whittled their shortlist down to three names at the moment.
Those names: Ken Watanabe, Morgan Freeman and Bill Nighy.
Watanabe, for those who forget, played the League of Assassins member who was claimed to be Ra's al Ghul in Batman Begins (before he died and the true Demon's Head was revealed to be Liam Neeson's character). In that same film, Freeman played Lucius Fox, a role he reprised in The Dark Knight and The Dark Knight Rises. Nighy is probably best known for his role in the Pirates of the Caribbean franchise, but he's also had memorable roles in Harry Potter and the Deathly Hallows Part 1, Love Actually and director Edgar Wright's Three Flavours Cornetto Trilogy.
The Ancient One is Doctor Strange's mentor, the previous Sorcerer Supreme, and also the man who trained the film's rumored villain, Baron Mordo.